After searching "oil" on this board, it seems to me there has been a problem with the oil sensor. Too bad no dipstick.
The service rep explained to me, 'of course there is a dipstick, we'll just check the level', not inspiring a lot of confidence in them.
There were 2 people on this board who had a problem with adding too much oil when this problem arose, and 1 had subsequent engine problems.
A more knowledgeable BMW service rep explained that they didn't have access to the TSB's at the moment ('internet access down'), and that he'd call me later today. At least the loaner is a Z4, although totally different from my new car.